Homework 2

Directions:

  1. Show each step of your work and fully simplify each expression.
  2. Turn in your answers in class on a physical piece of paper.
  3. Staple multiple sheets together.
  4. Feel free to use Desmos for graphing.

Answer the following:

  1. Simplify the following. Get rid of all negative exponents.
    1. $-2^4$
    2. $(-2)^4$
    3. $\dfrac{(4x)^{1/2}}{8x^{1/4}}$
    4. $(x(x+1))^{-1/2}$
    5. $\left(\dfrac{x^8y^{-2}}{(x-1)(x+2)^2}\right)^{-1/2}$
    6. $\left(\dfrac{x + y}{4x}\right)^{-1/2}$
    7. $\dfrac{xy^{-3}z}{(2x)^{-1}y^2z^{-2}}$
    8. $\dfrac{(x+1)(x+2)}{(x+1)^{-2}(x+2)^2(x+3)}$
    9. $\dfrac{\sqrt[3]{x^2}}{x^{2/3}}$
    10. $\dfrac{(-3)^4\sqrt{x}}{3^2\sqrt[3]{x}}$
    11. $\left(\dfrac{xy^2 + (x+1)^2}{(x+2)^2}\right)^0$
  2. State whether each pair of expressions are like terms or not.
    1. $3x^2$ and $4y$
    2. $3x^2$ and $4x$
    3. $x^3y$ and $4x^3y$
    4. $5(x+1)(x+2)$ and $-(x+1)(x+2)$
    5. $-100(3x-2)(4x^2+3)^2$ and $4(4x^2+3)^2(3x-2)$
  3. Expand and simplify each expression.
    1. $(2x^2 + 3x) + (3x^3 + 2x)$
    2. $(x+1)(x-2)$
    3. $(x^2 + 2x + 1)(x-2)$
    4. $(x^6 - x^5) -2(x^4 - x^3) - x(x^2 - x)$
    5. $2x(x-3) - (2x - 1)(x + 2)$
    6. $(x + 1)(x - 2) - (x + 1)$
    7. $(x + y - z - w)(x + y + z + w)$
  4. Factor the following expressions.
    1. $-2x^3 - x^2$
    2. $(x+3)^2(x-2) + (x+3)(x-2)^2$
    3. $x^2 + 5x + 6$
    4. $x^2 + 13x + 12$
    5. $2x^2 + 7x + 3$
    6. (skip) $2x^2yz + 7xyz + 3yz$
    7. (skip) $4a^2 - 9b^2$
    8. (skip) $x^4 - 1$
    9. (skip) $(x^2 + 1)^2 - 7(x^2 + 1) + 10$
    10. (skip) $x^3 + 4x^2 + x + 4$

    5. The remaining problems will be on next week's homework. Skip for now unless you want to get a head start.

  5. Perform the indicated operation and/or fully simplify. Get rid of all negative exponents.
    1. $\dfrac{4(x+3)(x-1)}{2(x-1)}$
    2. $\dfrac{x^2 + 2x + 1}{x^2 - 1}$
    3. $\dfrac{x^2h + 2xh + h}{h}$
    4. $2 + \dfrac{1}{x + 3}$
    5. $\dfrac{(x+h)^2 - x^2}{h}$
    6. $\dfrac{x^2 + 7x + 12}{x^2 + 3x + 2} \cdot \dfrac{x^2 + 5x + 6}{x^2 + 6x + 9}$